Natural proteins adopt complex folded configurations. How they reach their folded configurations is a subject of intense interest. In addition, proteins must maintain stability in their native configurations, and there are open questions about how this is achieved, especially by proteins that must survive harsh conditions. Proteins that adopt particularly complex structures provide unique insights into both of these questions. This proposal focuses on the discovery and analysis of proteins whose structures reveal topological complexity, such as knotting, and linking of protein chains. Such proteins provide valuable test cases and challenging questions in the areas of protein folding and stabilization. Until recently, the possibility of naturally knotted protein chains was considered so problematic as to be nearly forbidden. But recent computational analysis of the growing structural database has revealed a few deeply knotted protein folds, and these have drawn the interest of experimentalists and theorists alike. In this proposal: (1) Using a new algorithm, we reveal a novel type of topologically complexity in the database of known protein structures: slip-knots. These are cases where a knot is created by some part of the protein chain, while the chain in its entirety appears to be unknotted. These cases, of which we have identified several, have escaped previous knot analysis. (2) We add to the set of known topologically complex proteins by determining new structures from a particular organism where we have evidence that linking and knotting are relatively common; (3) We develop a protein design strategy for converting knotted proteins into unknotted ones and vice-versa, in order to provide a test bed for studying the stabilizing effects of complex topological features in proteins. Supporting biophysical experiments are included. Biomedical relevance: The connections between human disease and protein destabilization and unfolding are becoming increasingly clear. At the present time, there are still open questions about the rules and mechanisms of protein folding. The proteins to be studied here possess unique features that make them valuable in efforts to achieve a fundamental understanding of protein structure and stability. [unreadable] [unreadable] [unreadable]